Multipoint Okounkov bodies

Abstract

Starting from the data of a big line bundle $L$ on a projective manifold $X$ with a choice of $N\ge 1$ different points on $X$ we provide a new construction of $N$ Okounkov bodies which encodes important geometric features of ($L\to X,p_1,\dots ,p_N$) such as the volume of $L$, the (moving) multipoint Seshadri constant of $L$ at $p_1,\dots ,p_N$, and the possibility to construct Kähler packings centered at $p_1,\dots ,p_N$. Toric manifolds and surfaces are examined in detail.

Final version, to appear in "Annales de l'Institut Fourier"